can we travel by train from Beijing to Guangzhou? Is the train convenience? How much it cost?

what about by plane? Which one is nicer? and how much the plane fare? I like to see the view, some reccomend take train, but i think it will take about one day trip? is it correct?

plane would be fastest way, train would be most interesting way, you must go soft sleeper, it is about $90, check out ctrip.com for good plane tickets

Yes, definitely you can. In fact the train ride is pretty comfortable and you can see the big changes of geography between the northern and southern China. For more and detailed information, you can visit www.seat61.com/china.htm

If you can buy a sleeper ticket and you get enough time, by train is a good choice. It will take you about 20 hours to get to Guangzhou by train. The sleeper ticket is about 450 Yuan.

Actually, it's more like a 2 days ride by train and the cost will be either the same or more than going by plane.
The train is more leisurely and there are some scenic areas along the way, the soft sleeps are comfortable and there is more freedom in activities. The plane ride is about 5-6 hours and you won't see much but save a lot of time. Most domestic flight in China provides little to no amenities and the food is nothing to write home about.

Its a 22 hour train ride and there are several departing daily.

T15 Beijing Guangzhou 18:19
T29 Beijing Guangzhou 13:28
T97 Beijing Guangzhou

I recommend you get the soft sleeper which is US$82 per person. Hard sleeper is $53.

Check out the web sites below too.